Question: 5 1. Consider the matrix -3 4 0 0 2 (a) Find the eigenvalues of A. (b) Find the eigenspaces of A. (c) Diagonalize A.

5 1. Consider the matrix -3 4 0 0 2 (a) Find the eigenvalues of A. (b) Find the eigenspaces of A. (c) Diagonalize A. (I.e. write A as a product PDP- where D is diagonal.) 2. Do similar matrices have the same eigenvalues? Do row-equivalent matrices have the same eigenvalues? Explain your answers. 3. Make up a 2 x 2 matrix with "nice" entries (integers, not too big). Find the characteristic polynomial of your matrix. The plug your matrix into its own characteristic polynomial. What do you get? Assuming your matrix is diagonalizable, explain what happened

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